ctrttf.f

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*> \brief \b CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          TRANSR, UPLO
*       INTEGER            INFO, N, LDA
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( 0: LDA-1, 0: * ), ARF( 0: * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CTRTTF copies a triangular matrix A from standard full format (TR)
*> to rectangular full packed format (TF) .
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANSR
*> \verbatim
*>          TRANSR is CHARACTER*1
*>          = 'N':  ARF in Normal mode is wanted;
*>          = 'C':  ARF in Conjugate Transpose mode is wanted;
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension ( LDA, N )
*>          On entry, the triangular matrix A.  If UPLO = 'U', the
*>          leading N-by-N upper triangular part of the array A contains
*>          the upper triangular matrix, and the strictly lower
*>          triangular part of A is not referenced.  If UPLO = 'L', the
*>          leading N-by-N lower triangular part of the array A contains
*>          the lower triangular matrix, and the strictly upper
*>          triangular part of A is not referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the matrix A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] ARF
*> \verbatim
*>          ARF is COMPLEX array, dimension ( N*(N+1)/2 ),
*>          On exit, the upper or lower triangular matrix A stored in
*>          RFP format. For a further discussion see Notes below.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date June 2016
*
*> \ingroup complexOTHERcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  We first consider Standard Packed Format when N is even.
*>  We give an example where N = 6.
*>
*>      AP is Upper             AP is Lower
*>
*>   00 01 02 03 04 05       00
*>      11 12 13 14 15       10 11
*>         22 23 24 25       20 21 22
*>            33 34 35       30 31 32 33
*>               44 45       40 41 42 43 44
*>                  55       50 51 52 53 54 55
*>
*>
*>  Let TRANSR = 'N'. RFP holds AP as follows:
*>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
*>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
*>  conjugate-transpose of the first three columns of AP upper.
*>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
*>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
*>  conjugate-transpose of the last three columns of AP lower.
*>  To denote conjugate we place -- above the element. This covers the
*>  case N even and TRANSR = 'N'.
*>
*>         RFP A                   RFP A
*>
*>                                -- -- --
*>        03 04 05                33 43 53
*>                                   -- --
*>        13 14 15                00 44 54
*>                                      --
*>        23 24 25                10 11 55
*>
*>        33 34 35                20 21 22
*>        --
*>        00 44 45                30 31 32
*>        -- --
*>        01 11 55                40 41 42
*>        -- -- --
*>        02 12 22                50 51 52
*>
*>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
*>  transpose of RFP A above. One therefore gets:
*>
*>
*>           RFP A                   RFP A
*>
*>     -- -- -- --                -- -- -- -- -- --
*>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
*>     -- -- -- -- --                -- -- -- -- --
*>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
*>     -- -- -- -- -- --                -- -- -- --
*>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
*>
*>
*>  We next  consider Standard Packed Format when N is odd.
*>  We give an example where N = 5.
*>
*>     AP is Upper                 AP is Lower
*>
*>   00 01 02 03 04              00
*>      11 12 13 14              10 11
*>         22 23 24              20 21 22
*>            33 34              30 31 32 33
*>               44              40 41 42 43 44
*>
*>
*>  Let TRANSR = 'N'. RFP holds AP as follows:
*>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
*>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
*>  conjugate-transpose of the first two   columns of AP upper.
*>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
*>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
*>  conjugate-transpose of the last two   columns of AP lower.
*>  To denote conjugate we place -- above the element. This covers the
*>  case N odd  and TRANSR = 'N'.
*>
*>         RFP A                   RFP A
*>
*>                                   -- --
*>        02 03 04                00 33 43
*>                                      --
*>        12 13 14                10 11 44
*>
*>        22 23 24                20 21 22
*>        --
*>        00 33 34                30 31 32
*>        -- --
*>        01 11 44                40 41 42
*>
*>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
*>  transpose of RFP A above. One therefore gets:
*>
*>
*>           RFP A                   RFP A
*>
*>     -- -- --                   -- -- -- -- -- --
*>     02 12 22 00 01             00 10 20 30 40 50
*>     -- -- -- --                   -- -- -- -- --
*>     03 13 23 33 11             33 11 21 31 41 51
*>     -- -- -- -- --                   -- -- -- --
*>     04 14 24 34 44             43 44 22 32 42 52
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE ctrttf( TRANSR, UPLO, N, A, LDA, ARF, INFO )
*
*  -- LAPACK computational routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      CHARACTER          TRANSR, UPLO
      INTEGER            INFO, N, LDA
*     ..
*     .. Array Arguments ..
      COMPLEX            A( 0: lda-1, 0: * ), ARF( 0: * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
*     ..
*     .. Local Scalars ..
      LOGICAL            LOWER, NISODD, NORMALTRANSR
      INTEGER            I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          conjg, max, mod
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      normaltransr = lsame( transr, 'N' )
      lower = lsame( uplo, 'L' )
      IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
         info = -1
      ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'CTRTTF', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.LE.1 ) THEN
         IF( n.EQ.1 ) THEN
            IF( normaltransr ) THEN
               arf( 0 ) = a( 0, 0 )
            ELSE
               arf( 0 ) = conjg( a( 0, 0 ) )
            END IF
         END IF
         RETURN
      END IF
*
*     Size of array ARF(1:2,0:nt-1)
*
      nt = n*( n+1 ) / 2
*
*     set N1 and N2 depending on LOWER: for N even N1=N2=K
*
      IF( lower ) THEN
         n2 = n / 2
         n1 = n - n2
      ELSE
         n1 = n / 2
         n2 = n - n1
      END IF
*
*     If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
*     If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
*     N--by--(N+1)/2.
*
      IF( mod( n, 2 ).EQ.0 ) THEN
         k = n / 2
         nisodd = .false.
         IF( .NOT.lower )
     $      np1x2 = n + n + 2
      ELSE
         nisodd = .true.
         IF( .NOT.lower )
     $      nx2 = n + n
      END IF
*
      IF( nisodd ) THEN
*
*        N is odd
*
         IF( normaltransr ) THEN
*
*           N is odd and TRANSR = 'N'
*
            IF( lower ) THEN
*
*             SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
*             T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
*             T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
*
               ij = 0
               DO j = 0, n2
                  DO i = n1, n2 + j
                     arf( ij ) = conjg( a( n2+j, i ) )
                     ij = ij + 1
                  END DO
                  DO i = j, n - 1
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
               END DO
*
            ELSE
*
*             SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
*             T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
*             T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
*
               ij = nt - n
               DO j = n - 1, n1, -1
                  DO i = 0, j
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
                  DO l = j - n1, n1 - 1
                     arf( ij ) = conjg( a( j-n1, l ) )
                     ij = ij + 1
                  END DO
                  ij = ij - nx2
               END DO
*
            END IF
*
         ELSE
*
*           N is odd and TRANSR = 'C'
*
            IF( lower ) THEN
*
*              SRPA for LOWER, TRANSPOSE and N is odd
*              T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
*              T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
*
               ij = 0
               DO j = 0, n2 - 1
                  DO i = 0, j
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
                  DO i = n1 + j, n - 1
                     arf( ij ) = a( i, n1+j )
                     ij = ij + 1
                  END DO
               END DO
               DO j = n2, n - 1
                  DO i = 0, n1 - 1
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
               END DO
*
            ELSE
*
*              SRPA for UPPER, TRANSPOSE and N is odd
*              T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
*              T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
*
               ij = 0
               DO j = 0, n1
                  DO i = n1, n - 1
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
               END DO
               DO j = 0, n1 - 1
                  DO i = 0, j
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
                  DO l = n2 + j, n - 1
                     arf( ij ) = conjg( a( n2+j, l ) )
                     ij = ij + 1
                  END DO
               END DO
*
            END IF
*
         END IF
*
      ELSE
*
*        N is even
*
         IF( normaltransr ) THEN
*
*           N is even and TRANSR = 'N'
*
            IF( lower ) THEN
*
*              SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
*              T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
*              T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
*
               ij = 0
               DO j = 0, k - 1
                  DO i = k, k + j
                     arf( ij ) = conjg( a( k+j, i ) )
                     ij = ij + 1
                  END DO
                  DO i = j, n - 1
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
               END DO
*
            ELSE
*
*              SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
*              T1 -> a(k+1,0) ,  T2 -> a(k,0),   S -> a(0,0)
*              T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
*
               ij = nt - n - 1
               DO j = n - 1, k, -1
                  DO i = 0, j
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
                  DO l = j - k, k - 1
                     arf( ij ) = conjg( a( j-k, l ) )
                     ij = ij + 1
                  END DO
                  ij = ij - np1x2
               END DO
*
            END IF
*
         ELSE
*
*           N is even and TRANSR = 'C'
*
            IF( lower ) THEN
*
*              SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
*              T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
*              T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
*
               ij = 0
               j = k
               DO i = k, n - 1
                  arf( ij ) = a( i, j )
                  ij = ij + 1
               END DO
               DO j = 0, k - 2
                  DO i = 0, j
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
                  DO i = k + 1 + j, n - 1
                     arf( ij ) = a( i, k+1+j )
                     ij = ij + 1
                  END DO
               END DO
               DO j = k - 1, n - 1
                  DO i = 0, k - 1
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
               END DO
*
            ELSE
*
*              SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
*              T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
*              T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
*
               ij = 0
               DO j = 0, k
                  DO i = k, n - 1
                     arf( ij ) = conjg( a( j, i ) )
                     ij = ij + 1
                  END DO
               END DO
               DO j = 0, k - 2
                  DO i = 0, j
                     arf( ij ) = a( i, j )
                     ij = ij + 1
                  END DO
                  DO l = k + 1 + j, n - 1
                     arf( ij ) = conjg( a( k+1+j, l ) )
                     ij = ij + 1
                  END DO
               END DO
*
*              Note that here J = K-1
*
               DO i = 0, j
                  arf( ij ) = a( i, j )
                  ij = ij + 1
               END DO
*
            END IF
*
         END IF
*
      END IF
*
      RETURN
*
*     End of CTRTTF
*
      END